Problem $1.$ Compute each limit or state why it does not exist.

$($a$)\underset{x3}{lim}\frac{x^2-x-6}{x^2-9}$

$($b$)\underset{x3}{lim}\frac{3-x}{|x-3|}$

$($c$)\underset{x0}{lim}(x^2*sin(\frac{1}{x}))$

Problem $2.$ Use the definition of derivative to find $f^{\text{'}}(x)$ if $f(x)=\frac{x^{2}7}{3x-1}.$

Problem $3.$ Find an equation of the tangent line to the curve $y=x\frac{2}{x}$ at the point $P(2,3).$

Problem $4.$ Find values of a and $b$ such that $f(x)$ is continuous at all points in $R.$

$f(x)=\{\begin{array}{cc}\frac{x^2-4}{x-2},& x<mn>2</mn>\\ a{x}^2-bx& 3,& 2x<mn>3</mn>\\ 2x-a& b,& x3\end{array}$